The Effect of Base-Flow Changes on Kelvin-Helmholtz Instability and Noise Radiation in Jets

Abstract

Using linear stability analyses, a systematic approach is followed to determine modifications to the base flow of a jet that reduce the growth rate and phase speed of disturbances in the Kelvin-Helmholtz instability. This has the potential to reduce the sound radiated from wavepackets in the jet. For the two-dimensional Bickley jet, an adjoint-based sensitivity analysis is used to determine the sensitivity of the eigenvalues of the Orr-Sommerfeld equation to base-flow changes. The growth rate of the disturbances may be reduced by reducing the shearing near the points where the adjoint eigenfunction peaks. When targeting a reduction in the phase speed of the disturbances, the base flow also changes around the peak of the adjoint eigenfunction. It is seen that base-flow changes to reduce growth rate or phase speed at a certain frequency can have adverse effects at higher frequencies. The analysis of the two-dimensional jet is extended and applied to an axisymmetric round jet by solving the linearized Navier-Stokes equation and its adjoint, to determine the stability characteristics and the optimal base-flow changes. For the round jet, as for the 2D jet, the base flow changes around the peak of the axial adjoint eigenfunction, with growth-rate reductions obtained by reducing shearing at this point. Attempts to reduce the growth rate of disturbances are successful over a range of frequencies around the target frequency, but can have adverse effects at high frequencies. Also, upon increasing deviations between the modified velocity profile and the reference, a second mode becomes unstable and dominates the behaviour at high frequencies, leading to high growth rates. Attempts to reduce the phase speed do not have the same adverse high frequency effects, but do cause the growth rate to increase across a range of frequencies.